304 Mr. A. S. Davis on the Vibrations which Heated 

 From (8) and (9) we obtain 



6) — w' dt v ' 



But from (6), 



6) + ft)' 2 2. 2^ 

 ft) ft)' # 2 



Also 

 and 



ft) + ft) , ""F + 6 2T 



H =-0000 147 -xTa/it, 



^ _ -0000074 x T, . 



a2 _ -0000147x^(5-3) 



£ 2 + & 2 2^7rf + -0000147 xT ; 



In the rocker I have employed, # = 2*5 ; 6 = 22, c = 10 millims. 



Putting also # = 9800 and ir — -^-^ and reducing, we obtain 

 T,=10°C. very nearly. 



Thus we conclude that if, after each impact, the heated lead 

 and the cooled copper in the neighbourhood of the point of con- 

 tact were to regain their initial temperatures before the next 

 impact upon the same point took place, then a difference of only 

 10° C. between the two metals would be sufficient to keep up a 

 vibration of the rocker at the rate of 225 impacts per second. 

 This, of course, will not be the case; but it is not difficult to 

 see that, owing to the fact that the little masses of heated lead 

 and cooled copper are each half surrounded by metal, the reduc- 

 tion of the temperature of the metals to the temperature of the 

 surrounding metal by the process of conduction will take place 

 very rapidly. Thus if, just after the contact is broken, the heat 

 has spread through a portion of the lead (approximately hemi- 

 spherical) to a depth d, say, then before the contact is again 

 made the heat derived from the previous contact will have 

 spread to a depth a/2 . d, and will occupy a space approximately 

 2 V2 times that which it occupied when the last contact was 

 broken. Consequently the increment of temperature produced 



by the previous contact will be diminished to — -?*= of its former 



amount. 



In the same manner the increment of temperature gained by 

 the last contact but one will be diminished to about one eighth 

 of its former amount. Only a very few of the previous contacts 

 will therefore have any appreciable effect in causing the tempe- 

 ratures of the two metals at their points of contact to differ by a 



